An immuno-epidemiological model with waning immunity after infection or vaccination

Abstract

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immunoepidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of first order partial differential equations with different transfer velocities. This untypical feature makes the proved existence of a solution novel and non-trivial. The asymptotic behaviour of the model is analysed using the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and the costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.